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A047587 Numbers that are congruent to {0, 2, 3, 5, 6, 7} mod 8.

%I A047587 #17 Sep 08 2022 08:44:57
%S A047587 0,2,3,5,6,7,8,10,11,13,14,15,16,18,19,21,22,23,24,26,27,29,30,31,32,
%T A047587 34,35,37,38,39,40,42,43,45,46,47,48,50,51,53,54,55,56,58,59,61,62,63,
%U A047587 64,66,67,69,70,71,72,74,75,77,78,79,80,82,83,85,86,87
%N A047587 Numbers that are congruent to {0, 2, 3, 5, 6, 7} mod 8.
%H A047587 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047587 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047587 G.f.: x^2*(2+x+2*x^2+x^3+x^4+x^5)/((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).
%F A047587 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047587 a(n) = (24*n-15+3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/18.
%F A047587 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-8. (End)
%F A047587 Sum_{n>=2} (-1)^n/a(n) = (8-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - 3*(sqrt(2)-1)*Pi/16. - _Amiram Eldar_, Dec 27 2021
%p A047587 A047587:=n->(24*n-15+3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/18: seq(A047587(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047587 Select[Range[0,150], MemberQ[{0,2,3,5,6,7}, Mod[#,8]]&] (* _Harvey P. Dale_, Oct 04 2011 *)
%o A047587 (Magma) [n : n in [0..100] | n mod 8 in [0, 2, 3, 5, 6, 7]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y A047587 Cf. A047503, A047571.
%K A047587 nonn,easy
%O A047587 1,2
%A A047587 _N. J. A. Sloane_